# Category Archives: mathematics

## The Johnson-Lindenstrauss Lemma, and the paradoxical power of random linear operators. Part 1.

I’ll be discussing the ramifications of: William B. Johnson and Joram Lindenstrauss, “Extensions of Lipschitz mappings into a Hilbert space, Contemporary Mathematics, 26:189–206, 1984. for several posts here. Some introduction and links to proofs and explications will be provided, as … Continue reading

## Numbers, feelings, and imagination

“But numbers don’t make noises. They don’t have colours. You can’t taste them or touch them. They don’t smell of anything. They don’t have feelings. They don’t make you feel. And they make for pretty boring stories.” That’s from here, … Continue reading

## Sampling: Rejection, Reservoir, and Slice

An article by Suilou Huang for catatrophe modeler AIR-WorldWide of Boston about rejection sampling in CAT modeling got me thinking about pulling together some notes about sampling algorithms of various kinds. There are, of course, books written about this subject, … Continue reading

## Fast means, fast moments (originally devised 1984)

There are many devices available for making numerical calculations fast. Modern datasets and computational problems apply stylized architectures, and use approaches to problems including special algorithms for just calculating dominant eigenvectors or using non-classical statistical mechanisms like shrinkage to estimate … Continue reading

“One of the most interesting things about the MIP ensembles is that the mean of all the models generally has higher skill than any individual model.” We hold these truths to be self-evident, that all models are created equal, that … Continue reading

## These are ethical “AI Principles” from Google, but they might as well be `technological principles’

This is entirely adapted from this link, courtesy of Google and Alphabet. Objectives Be socially beneficial. Avoid creating or reinforcing unfair bias. Be built and tested for safety. Be accountable to people. Incorporate privacy design principles. Uphold high standards of … Continue reading

## When linear systems can’t be solved by linear means

Linear systems of equations and their solution form the cornerstone of much Engineering and Science. Linear algebra is a paragon of Mathematics in the sense that its theory is what mathematicians try to emulate when they develop theory for many … Continue reading

## The Rule of 135

From SingingBanana.

## Is the answer to the democratization of Science doing more Citizen Science?

I have been following, with keen interest, the post and comment thread pertaining to “Democratising science” at the blog I monitor daily, … and Then There’s Physics. I think the core subject being discussed is a little different from my … Continue reading

## Chesterton’s fence, ecological sensitivity, and the disruption of ecological services

Hat tip to Matt Levine for introducing me to the term Chesteron’s fence: Chesterton’s fence is the principle that reforms should not be made until the reasoning behind the existing state of affairs is understood. … In the matter of … Continue reading

## Happy Newtonmas!

When knowledge conquered fear … And, what better way to celebrate than watching the National Geographic Cosmos episode, When knowledge conquered fear, hosted by the great Dr Neil deGrasse Tyson, Director of the Hayden Planetarium in New York City.

## Cathy O’Neil’s WEAPONS OF MATH DESTRUCTION: A Review

(Revised and updated Monday, 24th October 2016.) Weapons of Math Destruction, Cathy O’Neil, published by Crown Random House, 2016. This is a thoughtful and very approachable introduction and review to the societal and personal consequences of data mining, data science, … Continue reading

## Polls, Political Forecasting, and the Plight of Five Thirty Eight

On 17th October 2016 AT 7:30 p.m., Nate Silver of FiveThirtyEight.com wrote about how, as former Secretary of State Hillary Clinton’s polling numbers got better, it was more difficult for FiveThirtyEight‘s models to justify increasing her probability of winning, although … Continue reading

## “All models are wrong. Some models are useful.” — George Box

(Image courtesy of the Damien Garcia.) As a statistician and quant, I’ve thought hard about that oft-cited Boxism. I’m not sure I agree. It’s not that there is such a thing as a perfect model, or correct model, whatever in … Continue reading

## Repaired R code for Markov spatial simulation of hurricane tracks from historical trajectories

I’m currently studying random walk and diffusion processes and their connections with random fields. I’m interested in this because at the core of dynamic linear models, Kalman filters, and state-space methods there is a random walk in a parameter space. … Continue reading

## “Holy crap – an actual book!”

Originally posted on mathbabe:

Yo, everyone! The final version of my book now exists, and I have exactly one copy! Here’s my editor, Amanda Cook, holding it yesterday when we met for beers: Here’s my son holding it: He’s offered…

## France, and Mathematics

Cédric Villani, does Mathematics. “Problems worthy of attack, prove their worth by hitting back.” — Piet Hein

## On Smart Data

One of the things I find surprising, if not astonishing, is that in the rush to embrace Big Data, a lot of learning and statistical technique has been left apparently discarded along the way. I’m hardly the first to point … Continue reading

## “Catching long tail distribution” (Ted Dunning)

One of the best presentations on what can happen if someone takes a naive approach to network data. It also highlights what is, to my mind, the greatly underappreciated t-distribution, which is typically only used in connection with frequentist Student … Continue reading

## Climate Denial Fails Pepsi Challenge

Originally posted on Climate Denial Crock of the Week:

Stephen Lewandowsky specializes in conducting research that pulls back the curtain climate denial psychology. He’s done it again. Washington Post: Researchers have designed an inventive test suggesting that the arguments commonly used…

## Cory Lesmeister’s treatment of Simson’s Paradox (at “Fear and Loathing in Data Science”)

(Updated 2016-05-08, to provide reference for plateaus of ML functions in vicinity of MLE.) Simpson’s Paradox is one of those phenomena of data which really give Statistics a substance and a role, beyond the roles it inherits from, say, theoretical … Continue reading

## “Lucky d20” (by Tamino, with my reblogging comments)

Originally posted on Open Mind:

What with talk of killer heat waves, droughts, floods, etc. etc., this blog tends to get pretty serious. When it does, we don’t deal with happy prospects, but with the danger of worldwide catastrophe. But…

## Of my favorite things …

(Clarifying language added 4 Apr 2016, 12:26 EDT.) I just watched an episode from the last season of Star Trek: The Next Generation entitled “Force of Nature.” As anyone who pays the least attention to this blog knows, opposing human … Continue reading

## patents disincentivize progress

Very interesting.

## “Grid shading by simulated annealing” [Martyn Plummer]

Source: Grid shading by simulated annealing (or what I did on my holidays), aka “fun with GCHQ job adverts”, by Martyn Plummer, developer of JAGS. Excerpt: I wanted to solve the puzzle but did not want to sit down with … Continue reading

## Ah, Hypergeometric!

(“Ah, Hypergeometric!” To be said with the same resignation and acceptance as in “I’ll burn my books–Ah, Mephistopheles!” from Faust.)😉 Dr John Cook, eminent all ’round statistician (with a specialty in biostatistics) and statistical consultant, took up a comment I … Continue reading

## high dimension Metropolis-Hastings algorithms

If attempting to simulate from a multivariate standard normal distribution in a large dimension, when starting from the mode of the target, i.e., its mean γ, leaving the mode γis extremely unlikely, given the huge drop between the value of the density at the mode γ and at likely realisations Continue reading

## Causal Diagrams

Like Sankey diagrams, causal diagrams are a useful tool to assess and communicate complicated systems and their intrarelationships: It’s possible to use these for analysis and prescription: Here is the (promised) presentation on reenforcing loops: So how can these techniques … Continue reading